Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 8x - 8$ and $ KL = 7x - 6$ Find $JL$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {8x - 8} = {7x - 6}$ Solve for $x$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 8({2}) - 8$ $ KL = 7({2}) - 6$ $ JK = 16 - 8$ $ KL = 14 - 6$ $ JK = 8$ $ KL = 8$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {8} + {8}$ $ JL = 16$